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Math and the Great White Whale: Your Guide to RNG (and why you STILL can't get the right VMA weapon)

Like most MMO's, Elder Scrolls online uses a lot of RNG for everything from combat to loot mechanics and soon maybe even monetization! But just what can RNG do for you? Well, that depends on exactly how "random" your tables are! Let's look at some common examples.

Everyone knows about the flip of a fair coin. On average you'll get 50% heads and 50% tails. And everyone knows about the roll of a fair die. 1/6 times you roll it you'll get some given number, 1/2 of the time you'll get an even number, and 1/2 of the time you'll get an odd number. But what about something more complex, like the amount of gold looted from an enemy or your chance at a Light Infused Molag Kena helm? Read further to find out!

Let's start with gold, because who doesn't love those shiny little devils? Gold drives the in-game economy and keeps our gear in good repair! But how often will you get it, and how much will you get WHEN you get it? Let's take a look at a sample loot table. Note that this isn't a real loot table from the game, it is an artificial one made to enhance understanding!

As you can see, there's a 2/3 chance that you'll get gold (4 out of the 6 entries have gold), but what's with the range on the entry? More random numbers! Under this model, 1/6 of the time you'll get 1-2 gold, 1/6 of the time you'll get 2-3 gold, and so on. This model can easily scale up based on player level by simply adding a level-based multiplier to the expression, so at level 50 it could become 50-100 gold 1/6 of the time, and 100-150 gold 1/6 of the time, etc. How-forward thinking!

"But wait!", you might say, "I remember combinatorics and statistics from high school, and I'm pretty sure those empty slots means that there's a chance you'll NEVER get gold!" Well, you are correct. But also wrong!! This is because you can tweak and RNG-based loot system to be slightly more fair while still maintaining a semblance of risk. For example, you can put a cap on the number of consecutive instances of not getting loot. You just increment a counter, and when you hit a certain number of enemies that didn't drop loot, you reduce your loot table to only contain actual instances of loot. Simple and very helpful!

If you don't do this, you are leaving yourself open to some very naughty happenings. As stated previously, there are circumstances where empty slots in your loot table will almost guarantee that as your playerbase increases, some people just won't ever get loot. It becomes more and more unlikely, but for a game like ESO with 7 million players, it can happen! Let's examine that by modeling the way Undaunted set helmets drop.

Currently (but soon to change!!) fighting certain dungeon bosses has a chance to drop a helmet from the undaunted set. The key phrase here is "a chance to drop". Let's say, as an example, that your boss monster drops a helm 1/4 of the time. You want to find out what your chances are for getting a helm by running the dungeon a certain number of times. This is very complicated math!! I won't try to make you understand it, but for fun it looks something like this!

Wow, what a mouthful! Of course, we don't actually need to do that. By being clever kittens, we can instead choose to figure out what your chances are for receiving nothing after a certain number of dungeon runs, and then take the compliment of that chance to obtain the chance of obtaining a helm!

That little bit at the end there means we can skip aaaaall that math and go straight for something easy that you can plug into the simplest of calculators! Take THAT, Texas Instruments! All you need to do is figure out the drop rate for a helm (25% in our example, or 0.25), subtract it from 1, and raise it to the power of the number of attempts, then subtract that from 1 again! So if we're running the dungeon 50 times, that's just 1 - 0.75^50, which is 0.99999943367. Great odds!!

Hmmm... something's wrong, though. We have 7 million players in our game, and climbing! If we multiply that by 7 million we should get the average number of people out of our 7 million who will obtain a helm after 50 runs. Uh oh! Only 6999996!! On average we're still leaving 4 people out if they all run the dungeon 50 times. Better luck next time, kids! I hope the meta doesn't change as soon as they finally get one.

But surely those 4 people just need to run a few more dungeons to be sure that they get the helm they want, right? Let's find out together! If they run 60 dungeons then on average 6999999 players will get the helm. Wow, already knocked 3 out of 4 off, surely just a few more will do it! At 70 dungeons it goes up to... 6999999 again. Hmm. 80? No, still 6999999. 100? No, still 6999999. A thousand? No. A million?? No!! Surely there must be some number that will do it, though, right? Well, no. Mathematically, you will never be sure! The chances of getting nothing get smaller and smaller the more you do it, but it is never guaranteed. And with 7 million players (and growing), it becomes much more likely that at least one person will lose out, no matter what you do or how often you run.
Adjusting the drop chance won't do it, either. As long as there is a chance for nothing, there is an chance for infinitely nothing.

That's one reason why the upcoming changes to Undaunted helms are so great!! By guaranteeing a Monster Mask reward for Veteran Dungeons, they've ensured that ALL players will get something good, no matter how bad your luck is! Of course, it's not all sunshine and rainbows. the armor type and trait are still random, after all. Thus, if someone needs something more specific than "a Monster Mask", we are back to guaranteeing that someone comes away upset. We simply redo the equation so that we only count the one trait/weight combo as "something" and everything else as "nothing". Still, most builds have at least a little leeway for trait/weight combos, as the most powerful feature of the sets tend to be the set bonuses, so even if you run the risk of never getting true Best In Slot for your build, you will no longer run the risk of getting truly "nothing".

As we've seen, a player's perception of what is valuable/useless can skew how we compute probabilities using our loot tables. For some, getting a Light Divines Molag Kena helm is just not enough, so we have to cross even that rare drop off their loot table when evaluating for the probability of getting "something" versus "nothing". This same principle affects RNG across all aspects of the game, including the ne Crown Crates!

As surely everyone's seen by now, Crown Crates are coming to the Crown Store. These items will always contain some amount of random consumables, and also have a chance to contain costumes, pets, and mounts! Pretty exciting for people who love random consumables, but maybe not for everybody. If you like random consumables, the probability of getting something you want in the crate is 100%! Congratulations!! If not, however, we have more math to do.

Let us consider the case of someone only wanting the rare mounts that will drop. Let us first consider the subset of this case where somebody only want one mount out of all the mounts that have a chance to drop. For this player, we can simply take the drop rate of the mount, subtract it from one, and raise it to the power of how many Crown Crates that player is willing to buy. Of course, we don't have the actual drop rates, so we'll work with some sample values instead! As for how many Crown Crates someone is willing or able to buy, we'll use another example!

Here is my current Crown balance. Gee willickers, what a haul! With this balance, I could buy 80 Crown Crates. Let's assume I spend all of my Crowns on Crown Crates for the sake of science! What a noble sacrifice, brings a tear to the eye and everything. Let's start with a 5% drop chance and go from there! Remember, we're calculating the odds of getting "nothing" since it's an easier computation. (1 - 0.05) to the 80th power is... 1.7%! Not bad, not bad, it's almost certain that we'll get it. But as we saw before, it is not certain, so the more number of people buying Crown Crates with this drop %, the more people who will walk away disappointed. If we round down that's only 1 player out of 100, but remember, 7 million players. That's quite a few individuals!! Let us also not forget that not many people will be able to buy 80 Crown Crates, and the fewer you buy the worse your chances will be.

Now, 5% drop rate seems pretty good, it might even be the actual drop rate for some of the discontinued mounts like the Polar Bear or the Clouded Senche, but what about the reaaaally rare mounts that have yet to be revealed? Let's assume a 1% drop chance. It's not stupidly rare, but it's far outside most peoples' playgrade. 80 Crown Crates, here we come!! (1 - 0.01) to the 80th power is... 44.8%!! Wait, WHAT?? But with a 5% drop rate it was only a 1.7% chance of failure, how did it grow so fast?? Well, that's a long and complicated mathematical discussion, but it serves to illustrate the point.

"Well, maybe you need to buy the full 100 Crown Crates, right?" you ask, plaintively. "I mean if it's a 1% drop chance then surely at 100 Crown Crates you'll get it down to only a 1% chance of failure!" Oh, you poor sweet dear. (1 - 0.01) to the 100th power is still a 36.6% chance of failure. "YO, BUT HOW MANY FOR 1%??" you ask, eyes wide in terror. 458.2, and since we can't buy partial Crown Crates we round this up to 459. And again, this is still leaving you with the same chance of failure as all of those individual Crown Crates had to drop the mount to begin with. Better luck next time!!

Obviously, however, some folks are going to want more than just the one mount! And also we don't know the drop rates so it might not be as bad as all that! It could also be worse than all that, I'm not going to sugarcoat the science or the uncertainty, but there is definitely more wiggle room than the 1% scenario. If, for instance, someone wants more than one thing from the Crown Crates, you can add up all the drop percentages to get your overall chance for failure. Let's look at an example.

If you want one mount that drops 5% of the time, another mount that drops 10% of the time, and a mount that drops 20% of the time, then technically you will get "something" at a 35% drop chance! If you buy 80 Crown Crates, that's (1 - 0.35) to the 80th power, which is a number so close to zero that you won't even recognize the notation for it unless you remember all of your highschool math. Naturally, it's not so low that there won't be, on average, someone who still fails despite the high drop chance, but it will happen very rarely. Maybe you don't want to buy 80 Crown Crates, though? Let's try just 40. Nope, still too close to zero to be worth mentioning! How about 20 Crown Crates? AHA!! EXPOSED! Oh, wait, that's 0.01% chance of failure. It's still going to be terrible for somebody, but it's very unlikely. Even by buying only 10 Crown Crates, you come out with only a 1.3% chance of getting nothing. So clearly the more things you actually want in the store and the better the drop chance of the individual items, the more likely your gamble will pay off.

Don't forget about Crown Gems! You can calculate your chance of getting Crown Gems if you know the drop rates of items already in your Collections UI. Then you can just plug that into the formula and find out your chance of failure to get Crown Gems (or, again, just subtract that from 100 to get your % chance of getting Crown Gems). If you consider Crown Gems to also be "something" instead of "nothing" you can even add it to your previous calculation regarding your overall chance of getting at least something you want, be it a mount, costume, pet, or Crown Gems.

Now, for some risk-averse players like myself, these RNG systems are all pretty scary and undesirable. ZOS has made great strides to modify the RNG so that as you complete the content you are more likely to be rewarded with something at least close to what you want, like the changes to Undaunted Helm drops. There's still some chance for a much narrower type of failure, but it is much better than a real chance of complete failure. This makes completing both new and old content much more rewarding from a progression standpoint, on top of the already thrilling feat of victorious combat. Other systems, which still offer a chance for what could be considered "complete failure", are less impressive. But at least now you can make a more informed decision while you interface with the various RNG systems in the game.

Here's that formula again, for anyone interested.

Also please don't just talk about the Crown Crates, I don't want this thread closed down for "duplication", lol. Mention the other systems as well!

“Kings of the land and the sky we are; proud gryphons.” Stalker stands, the epitome of pride. Naked and muscular, his wings widen and his feet dig in as if he alone holds down the earth and supports the heavens, keeping the two ever separate.”
Gryphons guild - @Milvan,

Like most MMO's, Elder Scrolls online uses a lot of RNG for everything from combat to loot mechanics and soon maybe even monetization! But just what can RNG do for you? Well, that depends on exactly how "random" your tables are! Let's look at some common examples.

Everyone knows about the flip of a fair coin. On average you'll get 50% heads and 50% tails. And everyone knows about the roll of a fair die. 1/6 times you roll it you'll get some given number, 1/2 of the time you'll get an even number, and 1/2 of the time you'll get an odd number. But what about something more complex, like the amount of gold looted from an enemy or your chance at a Light Infused Molag Kena helm? Read further to find out!

Let's start with gold, because who doesn't love those shiny little devils? Gold drives the in-game economy and keeps our gear in good repair! But how often will you get it, and how much will you get WHEN you get it? Let's take a look at a sample loot table. Note that this isn't a real loot table from the game, it is an artificial one made to enhance understanding!

As you can see, there's a 2/3 chance that you'll get gold (4 out of the 6 entries have gold), but what's with the range on the entry? More random numbers! Under this model, 1/6 of the time you'll get 1-2 gold, 1/6 of the time you'll get 2-3 gold, and so on. This model can easily scale up based on player level by simply adding a level-based multiplier to the expression, so at level 50 it could become 50-100 gold 1/6 of the time, and 100-150 gold 1/6 of the time, etc. How-forward thinking!

"But wait!", you might say, "I remember combinatorics and statistics from high school, and I'm pretty sure those empty slots means that there's a chance you'll NEVER get gold!" Well, you are correct. But also wrong!! This is because you can tweak and RNG-based loot system to be slightly more fair while still maintaining a semblance of risk. For example, you can put a cap on the number of consecutive instances of not getting loot. You just increment a counter, and when you hit a certain number of enemies that didn't drop loot, you reduce your loot table to only contain actual instances of loot. Simple and very helpful!

If you don't do this, you are leaving yourself open to some very naughty happenings. As stated previously, there are circumstances where empty slots in your loot table will almost guarantee that as your playerbase increases, some people just won't ever get loot. It becomes more and more unlikely, but for a game like ESO with 7 million players, it can happen! Let's examine that by modeling the way Undaunted set helmets drop.

Currently (but soon to change!!) fighting certain dungeon bosses has a chance to drop a helmet from the undaunted set. The key phrase here is "a chance to drop". Let's say, as an example, that your boss monster drops a helm 1/4 of the time. You want to find out what your chances are for getting a helm by running the dungeon a certain number of times. This is very complicated math!! I won't try to make you understand it, but for fun it looks something like this!

Wow, what a mouthful! Of course, we don't actually need to do that. By being clever kittens, we can instead choose to figure out what your chances are for receiving nothing after a certain number of dungeon runs, and then take the compliment of that chance to obtain the chance of obtaining a helm!

That little bit at the end there means we can skip aaaaall that math and go straight for something easy that you can plug into the simplest of calculators! Take THAT, Texas Instruments! All you need to do is figure out the drop rate for a helm (25% in our example, or 0.25), subtract it from 1, and raise it to the power of the number of attempts, then subtract that from 1 again! So if we're running the dungeon 50 times, that's just 1 - 0.75^50, which is 0.99999943367. Great odds!!

Hmmm... something's wrong, though. We have 7 million players in our game, and climbing! If we multiply that by 7 million we should get the average number of people out of our 7 million who will obtain a helm after 50 runs. Uh oh! Only 6999996!! On average we're still leaving 4 people out if they all run the dungeon 50 times. Better luck next time, kids! I hope the meta doesn't change as soon as they finally get one.

But surely those 4 people just need to run a few more dungeons to be sure that they get the helm they want, right? Let's find out together! If they run 60 dungeons then on average 6999999 players will get the helm. Wow, already knocked 3 out of 4 off, surely just a few more will do it! At 70 dungeons it goes up to... 6999999 again. Hmm. 80? No, still 6999999. 100? No, still 6999999. A thousand? No. A million?? No!! Surely there must be some number that will do it, though, right? Well, no. Mathematically, you will never be sure! The chances of getting nothing get smaller and smaller the more you do it, but it is never guaranteed. And with 7 million players (and growing), it becomes much more likely that at least one person will lose out, no matter what you do or how often you run.
Adjusting the drop chance won't do it, either. As long as there is a chance for nothing, there is an chance for infinitely nothing.

That's one reason why the upcoming changes to Undaunted helms are so great!! By guaranteeing a Monster Mask reward for Veteran Dungeons, they've ensured that ALL players will get something good, no matter how bad your luck is! Of course, it's not all sunshine and rainbows. the armor type and trait are still random, after all. Thus, if someone needs something more specific than "a Monster Mask", we are back to guaranteeing that someone comes away upset. We simply redo the equation so that we only count the one trait/weight combo as "something" and everything else as "nothing". Still, most builds have at least a little leeway for trait/weight combos, as the most powerful feature of the sets tend to be the set bonuses, so even if you run the risk of never getting true Best In Slot for your build, you will no longer run the risk of getting truly "nothing".

As we've seen, a player's perception of what is valuable/useless can skew how we compute probabilities using our loot tables. For some, getting a Light Divines Molag Kena helm is just not enough, so we have to cross even that rare drop off their loot table when evaluating for the probability of getting "something" versus "nothing". This same principle affects RNG across all aspects of the game, including the ne Crown Crates!

As surely everyone's seen by now, Crown Crates are coming to the Crown Store. These items will always contain some amount of random consumables, and also have a chance to contain costumes, pets, and mounts! Pretty exciting for people who love random consumables, but maybe not for everybody. If you like random consumables, the probability of getting something you want in the crate is 100%! Congratulations!! If not, however, we have more math to do.

Let us consider the case of someone only wanting the rare mounts that will drop. Let us first consider the subset of this case where somebody only want one mount out of all the mounts that have a chance to drop. For this player, we can simply take the drop rate of the mount, subtract it from one, and raise it to the power of how many Crown Crates that player is willing to buy. Of course, we don't have the actual drop rates, so we'll work with some sample values instead! As for how many Crown Crates someone is willing or able to buy, we'll use another example!

Here is my current Crown balance. Gee willickers, what a haul! With this balance, I could buy 80 Crown Crates. Let's assume I spend all of my Crowns on Crown Crates for the sake of science! What a noble sacrifice, brings a tear to the eye and everything. Let's start with a 5% drop chance and go from there! Remember, we're calculating the odds of getting "nothing" since it's an easier computation. (1 - 0.05) to the 80th power is... 1.7%! Not bad, not bad, it's almost certain that we'll get it. But as we saw before, it is not certain, so the more number of people buying Crown Crates with this drop %, the more people who will walk away disappointed. If we round down that's only 1 player out of 100, but remember, 7 million players. That's quite a few individuals!! Let us also not forget that not many people will be able to buy 80 Crown Crates, and the fewer you buy the worse your chances will be.

Now, 5% drop rate seems pretty good, it might even be the actual drop rate for some of the discontinued mounts like the Polar Bear or the Clouded Senche, but what about the reaaaally rare mounts that have yet to be revealed? Let's assume a 1% drop chance. It's not stupidly rare, but it's far outside most peoples' playgrade. 80 Crown Crates, here we come!! (1 - 0.01) to the 80th power is... 44.8%!! Wait, WHAT?? But with a 5% drop rate it was only a 1.7% chance of failure, how did it grow so fast?? Well, that's a long and complicated mathematical discussion, but it serves to illustrate the point.

"Well, maybe you need to buy the full 100 Crown Crates, right?" you ask, plaintively. "I mean if it's a 1% drop chance then surely at 100 Crown Crates you'll get it down to only a 1% chance of failure!" Oh, you poor sweet dear. (1 - 0.01) to the 100th power is still a 36.6% chance of failure. "YO, BUT HOW MANY FOR 1%??" you ask, eyes wide in terror. 458.2, and since we can't buy partial Crown Crates we round this up to 459. And again, this is still leaving you with the same chance of failure as all of those individual Crown Crates had to drop the mount to begin with. Better luck next time!!

Obviously, however, some folks are going to want more than just the one mount! And also we don't know the drop rates so it might not be as bad as all that! It could also be worse than all that, I'm not going to sugarcoat the science or the uncertainty, but there is definitely more wiggle room than the 1% scenario. If, for instance, someone wants more than one thing from the Crown Crates, you can add up all the drop percentages to get your overall chance for failure. Let's look at an example.

If you want one mount that drops 5% of the time, another mount that drops 10% of the time, and a mount that drops 20% of the time, then technically you will get "something" at a 35% drop chance! If you buy 80 Crown Crates, that's (1 - 0.35) to the 80th power, which is a number so close to zero that you won't even recognize the notation for it unless you remember all of your highschool math. Naturally, it's not so low that there won't be, on average, someone who still fails despite the high drop chance, but it will happen very rarely. Maybe you don't want to buy 80 Crown Crates, though? Let's try just 40. Nope, still too close to zero to be worth mentioning! How about 20 Crown Crates? AHA!! EXPOSED! Oh, wait, that's 0.01% chance of failure. It's still going to be terrible for somebody, but it's very unlikely. Even by buying only 10 Crown Crates, you come out with only a 1.3% chance of getting nothing. So clearly the more things you actually want in the store and the better the drop chance of the individual items, the more likely your gamble will pay off.

Don't forget about Crown Gems! You can calculate your chance of getting Crown Gems if you know the drop rates of items already in your Collections UI. Then you can just plug that into the formula and find out your chance of failure to get Crown Gems (or, again, just subtract that from 100 to get your % chance of getting Crown Gems). If you consider Crown Gems to also be "something" instead of "nothing" you can even add it to your previous calculation regarding your overall chance of getting at least something you want, be it a mount, costume, pet, or Crown Gems.

Now, for some risk-averse players like myself, these RNG systems are all pretty scary and undesirable. ZOS has made great strides to modify the RNG so that as you complete the content you are more likely to be rewarded with something at least close to what you want, like the changes to Undaunted Helm drops. There's still some chance for a much narrower type of failure, but it is much better than a real chance of complete failure. This makes completing both new and old content much more rewarding from a progression standpoint, on top of the already thrilling feat of victorious combat. Other systems, which still offer a chance for what could be considered "complete failure", are less impressive. But at least now you can make a more informed decision while you interface with the various RNG systems in the game.

Here's that formula again, for anyone interested.

Also please don't just talk about the Crown Crates, I don't want this thread closed down for "duplication", lol. Mention the other systems as well!

Actually great example of making a completely math focused thread, but making it entertaining enough to read all the way through:) thank you, I thoroughly enjoyed it.

Great stuff! I really like the recent and upcoming changes to various things that change the loot drop percentage to 100% as, like you say, it completely gets rid of the problem of a small portion of the population having to run dungeons 50, 100, 200 times to get just one item loot. You still have to farm things to get your desired/BiS trait but at least you have something you can use.

Is the value you used of 25% drop for monster helms drop rate made up or verified? I did a similar analysis a couple of times and seemed to run into the unofficial stats of 5-10% drop for monster helms which seems to more match what I've encountered. With a 5% drop rate and a 7 million population size the number of runs needed for some people to get one helm to drop is on the north side of crazy.

Also please don't just talk about the Crown Crates, I don't want this thread closed down for "duplication", lol. Mention the other systems as well!

:takes asprin and has more coffee:

Thank you for the explanation of how the rng works. [my personal explanation were RNG gremlins in the computer that hate me] Your explanation sounds much better. I wasn't going to touch the rng boxes before, now I have a much better reason for not even attempting to get one. And yes, I wanted to buy the clouded and the leopard senche. I was willing to pay the cost for them, but I'm not going to pay for the rng gamble boxes in an attempt to get them.

Great stuff! I really like the recent and upcoming changes to various things that change the loot drop percentage to 100% as, like you say, it completely gets rid of the problem of a small portion of the population having to run dungeons 50, 100, 200 times to get just one item loot. You still have to farm things to get your desired/BiS trait but at least you have something you can use.

Is the value you used of 25% drop for monster helms drop rate made up or verified? I did a similar analysis a couple of times and seemed to run into the unofficial stats of 5-10% drop for monster helms which seems to more match what I've encountered. With a 5% drop rate and a 7 million population size the number of runs needed for some people to get one helm to drop is on the north side of crazy.

I have no idea what the drops rate is for the monster helms.. but my gut feeling is telling me it's probably lower than 25%.

I ran Cradle of Shadow 11 times and only got 1 Velidreth Helm (Light - Prosperous.. how can end game gear drop in those crappy trait is astonishing..). 1 friend got it twice in first 4 runs while another friend never got it in about 8 runs now.

When farming Malubeth a few months ago, it took me 8 runs to get it.
But a friend farming it with me got it 4 times in a row (no joke).

That's the only data I have kept when farming monster pieces.

PSN: sluiceqc (NA-PS4) CP: 551+I strictly play on Daggerfall Covenant for when it comes to PvP

And see, the problem is right there in the picture accompanying all the math. It's the cat's fault! If you put the cats in charge of the RNG it just causes problems. The die rolls, the cat bats it, the number changes, the cat bats it, it rolls under the sofa and you get nothing. I love furries but they can be an issue sometimes.

Great thread. I'm mostly interested in the probability of getting a certain Maelstrom Weapon, as you can see in my thread here. (I don't provide crazy math because I'm a dummy)

@Recremen, you Math Guru, let me know if I did the math right for this!
For example, I will take the odds of getting a 2H sharpened Maelstrom weapon.
The odds are 3/96. Therefore 3.125% or 0.3125

Probability of getting it in 20 runs.
1 - (0.325) ^ 20 = ~0.53

So 53% chance of failure.. Meaning 47% chance of success.. Close to the median...

Probability of getting it in 50 runs.
1 - (0.325) ^ 50 = ~0.2

Meaning 80% chance of success.. Now I like those odds... As most will get it before their 50th run.

Probability of getting it in 100 runs

1 - (0.325) ^ = 100 = ~0.04

Meaning 96% chance to get it in 100 runs.

You arrived at the correct answers, but be careful with your percent conversions! You did them correctly in the calculator but here you wrote 0.325 instead of 0.0325. Important difference! Additionally, you'll want to write (1- 0.0325) ^ 20, not 1 - (0.0325) ^ 20. PEMDAS and all. But again, yes, you got them right in your calculator so you've arrived at the correct solution.

Great thread. I'm mostly interested in the probability of getting a certain Maelstrom Weapon, as you can see in my thread here. (I don't provide crazy math because I'm a dummy)

@Recremen, you Math Guru, let me know if I did the math right for this!
For example, I will take the odds of getting a 2H sharpened Maelstrom weapon.
The odds are 3/96. Therefore 3.125% or 0.3125

Probability of getting it in 20 runs.
1 - (0.325) ^ 20 = ~0.53

So 53% chance of failure.. Meaning 47% chance of success.. Close to the median...

Probability of getting it in 50 runs.
1 - (0.325) ^ 50 = ~0.2

Meaning 80% chance of success.. Now I like those odds... As most will get it before their 50th run.

Probability of getting it in 100 runs

1 - (0.325) ^ = 100 = ~0.04

Meaning 96% chance to get it in 100 runs.

You arrived at the correct answers, but be careful with your percent conversions! You did them correctly in the calculator but here you wrote 0.325 instead of 0.0325. Important difference! Additionally, you'll want to write (1- 0.0325) ^ 20, not 1 - (0.0325) ^ 20. PEMDAS and all. But again, yes, you got them right in your calculator so you've arrived at the correct solution.

NICE. LOL... Funny thing is I've been searching for this thing all morning.
And next thing I know a specific thread with what I'm searching..

And yeah I wrote everything too quickly, in here.. but done the calculation according to PEMDAS

Thanks again!

PSN: sluiceqc (NA-PS4) CP: 551+I strictly play on Daggerfall Covenant for when it comes to PvP

Great stuff! I really like the recent and upcoming changes to various things that change the loot drop percentage to 100% as, like you say, it completely gets rid of the problem of a small portion of the population having to run dungeons 50, 100, 200 times to get just one item loot. You still have to farm things to get your desired/BiS trait but at least you have something you can use.

Is the value you used of 25% drop for monster helms drop rate made up or verified? I did a similar analysis a couple of times and seemed to run into the unofficial stats of 5-10% drop for monster helms which seems to more match what I've encountered. With a 5% drop rate and a 7 million population size the number of runs needed for some people to get one helm to drop is on the north side of crazy.

Totally made up the 25% drop rate just to keep it simple, and to save the more disheartening percentages like 5% and 1% for later, when they'd have more impact. It's like storytelling, but with equations! I can change the wording around the 25% drop rate to make it more clear that it's just an example and not a confirmed current rate.

Yeah, RNG is a wonder - i have a 80% force lockpicking perk on simple chests, and i had occasions when it took me 4 and 5 attempts to get it open.

To be fair, it only happened twice - normally they open on first or second attempt, but still... 80% chance, mind you!

Skye Cloude - Sorc DPS, Master Crafter. Main, the bestestLae Lenne - Templar Healer Trial grade.Dromede - Stamina Nightblade, she's a newb and doesn't know what she's doingV'oghatta - Stamplar pretending to be a tankUlville Thonvella - aspiring Fire Mage, be careful around her fire sticks!Dromedaris - lost and not found. Named after a shoe, what else can you expect from her? A proper tank in her wildest dreamsSwims-Naked - too pretty to grind, too silly to quest.Sun Flair - Dunmer Templar that can't spell for life. To bad she's too broke to afford a name change... Well, at least she's pretty...

OK I am going to be honest here that I decided to read and reply because I saw a Khajiit (!?) holding a cat playing dices...... lol

Seriously though thanks for making a wall of elements (Maths and text) explaining the issue of the current looting system; it is a great thread with lots of lots of effort.

To make a short, the problem of the current looting system and the upcoming Crown Crates is you are not guaranteed with your desired item no matter how much time/ effort/ money are spent. Almost everything is a gamble in this game. While it works OK for BoE items since gold is easy to farm in this game, it makes (solo/ 4-man/ 12-man) trials not as enjoyable as they could have been with vMA being the most painful with group trades introduced since there is no one else but only you in the arena fighting mobs again, again and again... forever alone... no friends... no hugs like those in the twins in vMoL which gives you a great parse (your healers need some love... hug them!)

The same will go for the Crown Crates if exclusive items are introduced in the crates since it is bound to your account.

The solution to Crown Crates is rather simple, in my opinion, is that ZoS you can simply promise us you will not put any item exclusive to Crown Crates. Putting time limited items in the past is fine since you need to make some money, but, no items only exclusive to Crown Crates please. We want to enjoy this game, not to gamble. Just make everything be able to purchase with a fixed amount of crowns and add them into the Crown Crates if you want to lure people to try their luck and thus making more money which is necessary to run this game. You can make your money and the players who want their things are happy, isn't it a win-win situation?

For in-game BoP items, this is more tricky because two of the most important reasons that an item is BoP is you want us to earn it in a rightful way and making players want to return to the same content again and again. This is all good, I can definitely see the honour of getting yourself a special item by forcing them to complete a certain content and I can definitely understand the need of forcing the players to run the same content again and again to make this game lives on and encouraging them to improve their performance in trials.

HOWEVER, the current looting system needs some improvements. Forcing players to redo contents is OK, but sometimes it is just too much. From the developer side it may seem right but we players simply don't have hundreds of copies of ourselves so that the distribution of items you got could be very very different from each of us.

Seriously many suggestions are made before but to list some a token system, a smarter looting system and removal of T R A S H traits from the looting table are some possible improvements.

Again, please respect your players, don't make players who throw tons of time into completing your content left unrewarded (a decisive vMA bow and a vMA lighting staff are NOT rewarding, just to throw an example how horrible majority of the weekly rewards can be; oh and please give vDSA rewards to vDSA weeklies tyvm). While I (and many of us I guess) enjoy replaying a content to improve myself, there is a point where a content becomes boring and I want to move onto other aspects like getting my Master Angler achievement. Please make this game more enjoyable to play. Thanks everyone who read my post up to this point.

Great thread. I'm mostly interested in the probability of getting a certain Maelstrom Weapon, as you can see in my thread here. (I don't provide crazy math because I'm a dummy)

@Recremen, you Math Guru, let me know if I did the math right for this!
For example, I will take the odds of getting a 2H sharpened Maelstrom weapon.
The odds are 3/96. Therefore 3.125% or 0.3125

Probability of getting it in 20 runs.
1 - (0.325) ^ 20 = ~0.53

So 53% chance of failure.. Meaning 47% chance of success.. Close to the median...

Probability of getting it in 50 runs.
1 - (0.325) ^ 50 = ~0.2

Meaning 80% chance of success.. Now I like those odds... As most will get it before their 50th run.

Probability of getting it in 100 runs

1 - (0.325) ^ = 100 = ~0.04

Meaning 96% chance to get it in 100 runs.

You arrived at the correct answers, but be careful with your percent conversions! You did them correctly in the calculator but here you wrote 0.325 instead of 0.0325. Important difference! Additionally, you'll want to write (1- 0.0325) ^ 20, not 1 - (0.0325) ^ 20. PEMDAS and all. But again, yes, you got them right in your calculator so you've arrived at the correct solution.

NICE. LOL... Funny thing is I've been searching for this thing all morning.
And next thing I know a specific thread with what I'm searching..

And yeah I wrote everything too quickly, in here.. but done the calculation according to PEMDAS

Yes, that is quite possible! I didn't go over distributions or anything like that since it would overcomplicate things, and because people tend to experience things like the Optimism Bias and believe they they will fall on the lower-end of the distribution, instead of randomly falling anywhere on the distribution. By phrasing it in the manner of "someone will not be able to do this" and "a certain number of people are likely to experience this", I am hoping that it will switch the narrative from the personal to the general, letting people start to empathize wtih these "other" who actually will be on the upper end of a distribution.

Unless you're referring to my clickbaity title, in which case I apologize.

nice cut and paste on the stats theory...... statistical models need to be taken with a pinch of salt.

because....

there is a difference between the model and reality.

the map is not the territory.

I think I was pretty consistent describing the data surrounding the probabilities as being "likely" and not being guaranteed, so I'm not really sure what you're getting at. And with a population size of 7 million people, exactly how much variance from the model are you expecting, really? Let's not act like probability has no ability to convey meaningful information, we see the effects of it every day on the forums every time a new Maelstrom Weapon thread pops up.

Great thread. I'm mostly interested in the probability of getting a certain Maelstrom Weapon, as you can see in my thread here. (I don't provide crazy math because I'm a dummy)

@Recremen, you Math Guru, let me know if I did the math right for this!
For example, I will take the odds of getting a 2H sharpened Maelstrom weapon.
The odds are 3/96. Therefore 3.125% or 0.3125

Probability of getting it in 20 runs.
1 - (0.325) ^ 20 = ~0.53

So 53% chance of failure.. Meaning 47% chance of success.. Close to the median...

Probability of getting it in 50 runs.
1 - (0.325) ^ 50 = ~0.2

Meaning 80% chance of success.. Now I like those odds... As most will get it before their 50th run.

Probability of getting it in 100 runs

1 - (0.325) ^ = 100 = ~0.04

Meaning 96% chance to get it in 100 runs.

You arrived at the correct answers, but be careful with your percent conversions! You did them correctly in the calculator but here you wrote 0.325 instead of 0.0325. Important difference! Additionally, you'll want to write (1- 0.0325) ^ 20, not 1 - (0.0325) ^ 20. PEMDAS and all. But again, yes, you got them right in your calculator so you've arrived at the correct solution.

NICE. LOL... Funny thing is I've been searching for this thing all morning.
And next thing I know a specific thread with what I'm searching..

And yeah I wrote everything too quickly, in here.. but done the calculation according to PEMDAS

Thanks again!

And just like that, I have lost all motivation to run VMA...

Actually, call me crazy... but it somehow motivates me, as it proves that it's possible.

I mean, just looking at the odds from 1 run, it surely isn't motivating.
But looking at the odds from 20 or 50 runs... I like those.

I guess that is our "Token system".

PSN: sluiceqc (NA-PS4) CP: 551+I strictly play on Daggerfall Covenant for when it comes to PvP

OK I am going to be honest here that I decided to read and reply because I saw a Khajiit (!?) holding a cat playing dices...... lol

Seriously though thanks for making a wall of elements (Maths and text) explaining the issue of the current looting system; it is a great thread with lots of lots of effort.

To make a short, the problem of the current looting system and the upcoming Crown Crates is you are not guaranteed with your desired item no matter how much time/ effort/ money are spent. Almost everything is a gamble in this game. While it works OK for BoE items since gold is easy to farm in this game, it makes (solo/ 4-man/ 12-man) trials not as enjoyable as they could have been with vMA being the most painful with group trades introduced since there is no one else but only you in the arena fighting mobs again, again and again... forever alone... no friends... no hugs like those in the twins in vMoL which gives you a great parse (your healers need some love... hug them!)

The same will go for the Crown Crates if exclusive items are introduced in the crates since it is bound to your account.

The solution to Crown Crates is rather simple, in my opinion, is that ZoS you can simply promise us you will not put any item exclusive to Crown Crates. Putting time limited items in the past is fine since you need to make some money, but, no items only exclusive to Crown Crates please. We want to enjoy this game, not to gamble. Just make everything be able to purchase with a fixed amount of crowns and add them into the Crown Crates if you want to lure people to try their luck and thus making more money which is necessary to run this game. You can make your money and the players who want their things are happy, isn't it a win-win situation?

For in-game BoP items, this is more tricky because two of the most important reasons that an item is BoP is you want us to earn it in a rightful way and making players want to return to the same content again and again. This is all good, I can definitely see the honour of getting yourself a special item by forcing them to complete a certain content and I can definitely understand the need of forcing the players to run the same content again and again to make this game lives on and encouraging them to improve their performance in trials.

HOWEVER, the current looting system needs some improvements. Forcing players to redo contents is OK, but sometimes it is just too much. From the developer side it may seem right but we players simply don't have hundreds of copies of ourselves so that the distribution of items you got could be very very different from each of us.

Seriously many suggestions are made before but to list some a token system, a smarter looting system and removal of T R A S H traits from the looting table are some possible improvements.

Again, please respect your players, don't make players who throw tons of time into completing your content left unrewarded (a decisive vMA bow and a vMA lighting staff are NOT rewarding, just to throw an example how horrible majority of the weekly rewards can be; oh and please give vDSA rewards to vDSA weeklies tyvm). While I (and many of us I guess) enjoy replaying a content to improve myself, there is a point where a content becomes boring and I want to move onto other aspects like getting my Master Angler achievement. Please make this game more enjoyable to play. Thanks everyone who read my post up to this point.

You bring up a lot of good ideas! An alternative to a token system that keeps mostly to the original RNG model is to simply have a per-character reward tracker. Once someone is given some specific reward, like a Defending Maelstrom Bow, that gets removed from the loot table until they've gotten all possible rewards, at which point it resets. This keeps things RNG while preventing double-dipping on rewards, which means there IS some finite number of runs you need to complete before being guaranteed to get your desired weapon/Monster Mask/etc. SO even if they keep all 8 standard traits on the loot table, you know that if you do a full 96 runs then you'll finally get the thing. And I'm pretty sure ZOS isn't expecting folks to plow through 96 VMA runs to begin with, so this actually seems like a very good solution overall.

I have done like 15 VMA runs so far and still haven't seen dual wield weapons, ice and shock staves. I've gotten everything else with diferent traits. Most common traits are charged, infused and defending in my personal experience.

Wait their not 7 million active players only 7 million accounts that were created for this game wouldn't that increase the drop chance plus even if the 7 million was active I believe less than half actually do dungeons on a regular basis. Good number of players in this game prefer to play solo and than you have PVP players.So would that in case the chance of getting a drop or lower it?

And see, the problem is right there in the picture accompanying all the math. It's the cat's fault! If you put the cats in charge of the RNG it just causes problems. The die rolls, the cat bats it, the number changes, the cat bats it, it rolls under the sofa and you get nothing. I love furries but they can be an issue sometimes.

Do not blame Khajiit for the bad items you get. Shiny things that move need batting...

Dark Flare is the Beginning, Radiant is the End. Hail the Light Bringers!

Very interesting! Thanks for taking the time to explain it for non math wizzes like me.

I kinda like the monster helm drop rates the way they are. Mind you, I don't have all of the sets I want.
But after update 12, special sets won't be special anymore, because everyone will have them.

In regards to the crates: I don't like the risk/reward. No way I'll ever buy one.

I don't think any of them are really special anymore as most are easily obtainable and the few that aren't can be bought from cyrodil vendor.

I personally don't care if everyone in the game has the same items as me as I don't have that need to be a special snowflake.

This need to be a special snowflake is the true reason you see people complain when content is made easier, and not the often used cover of wanting a "challenge".

On to the op post.

I think the part about not being able to obtain the monster helm you want is atleast a little negated by the fact we can now trade with our group members.
As far as the shoulders are concerned I guess we will have to wait and see exactly how the new undaunted system will be implemented.

I read a great deal of your post but this is probably one of the longer post I have read in a while. Majority made for an interesting read.

Wait their not 7 million active players only 7 million accounts that were created for this game wouldn't that increase the drop chance plus even if the 7 million was active I believe less than half actually do dungeons on a regular basis. Good number of players in this game prefer to play solo and than you have PVP players.So would that in case the chance of getting a drop or lower it?

It does neither, the drop chance is a constant based on the layout of the loot tables. However!! It does change the overall player experience. If we don't actually have 7 million active players, then the deviation from the model will be more extreme. So as an individual you're still just as likely to get or not get a desired item from a dungeon, VMA, or Crown Crate, but the effects of deviation from the model across the entire population will be more acutely felt. It's kind of hard to describe if you aren't familiar with statistics and probability, though.